GRD Journals- Global Research and Development Journal for Engineering | Volume 3 | Issue 3 | February 2018 ISSN: 2455-5703
A Mathematical Model on Vorinostat (Histone Deacetylase Inhibitor) in Combination with Radiotherapy R. Lalitha Research Scholar Department of Applied Science AVVM Sri Pushpam College, Poondi
G. Komahan Research Adviser Department of Applied Science AVVM Sri Pushpam College, Poondi
Abstract There are four main and most types of cancer treatments, which are surgery, chemotherapy, radiotherapy, and immunotherapy. In this paper, we consider cancer treatment by radiotherapy. Radiation therapy is a treatment procedure that uses radiation to kill tumor cells. The Histone deacetylases inhibitor (HDAC) Vorinostat (suberoylanilide hydroxamic acid or SAHA) combination with radiotherapy blocks cancer cell proliferation. In this study we developed and analyse Mathematical model for tumor growth and histone deacetylase inhibitor, in combination with radiotherapy then we analyse the stability of equilibria. And fitting Patient 1 data to numerical simulation for locally weighted smoothing linear regression. Keywords- Histone Deacetylase Inhibitors, Radiation Therapy, Mathematical Model
I. INTRODUCTION Cancer treatment includes many physical therapeutic agents, all having the same basic shrinkage of tumor: to directly kill tumor cells or prevent their proliferation. Radiation may be used to cure or shrink early-stage cancer, stop cancer from coming back, or to treat symptoms when cancer has spread. Radiation therapy uses high-energy particles or waves, such as x-rays, gamma rays, electron beams, or protons, to destroy or damage cancer cells. But Radiation therapy is not a common way to treat colon cancer, though it may be used in certain circumstances. In advanced stages of colon cancer, radiation therapy is often given instead of surgery when an operation cannot be performed depending on patient’s age that means above Septuagenarian. Radiation may be used in combination with surgery as definitive therapy, or may be used to shrink tumor, or providing relief from the symptoms of colorectal cancer such as pain, bleeding, or blockage. Radiation therapy is sometimes given prior to surgery to improve outcomes in selected patients with rectal cancer. Radiation may be used to shrink a tumor before surgery or destroy any remaining cancer cells after removal. Cells are normally proliferating and divide in to form new cells. But cancer cells grow and divide faster than most normal cells. Radiation helps by making small breaks in the DNA inside cells. These breaks keep cancer cells from proliferating and dividing and cause them to die.
II. MODEL FORMULATION Consider the Logistic growth model describes tumor growth and the treatment doses đ?‘‘đ?‘‡ đ?‘‡ = đ?œ†đ?‘‡ (1 − ) − đ?œ‰đ?‘‰đ?‘‡ − đ?œ?đ?‘…(đ?‘Ą)đ?‘‡ (1) đ?‘‘đ?‘Ą đ??ž đ?‘‘đ?‘‰ = đ?‘”(đ?‘Ą) − đ?›żđ?‘‰ (2) đ?‘‘đ?‘Ą Where Îť - Tumor growth rate, negative growth rate indicates that the tumor population is decreasing K– Carrying capacity 0≤đ?œ‰â‰¤1 –HDAC induces a continuous tumor cell kill with the degree of intensity 0≤đ?œ‰â‰¤1 đ?‘”(đ?‘Ą)- Concentration of the drug. δ- Natural death of HDAC cells. Where đ?‘Ą
đ?‘”(đ?‘Ą) = âˆŤ đ?‘Ž(đ?‘Ąâ€˛) đ?‘’ (−đ?›ź(đ?‘Ąâˆ’đ?‘Ąâ€˛)) đ?‘‘đ?‘Ąâ€˛
(3)
0
�(�′) -the rate of given of HDAC concentration at time t’. � - Substance is completely removed per unit time.
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